We are excited to announce the TSVP Thematic Program "Singularities and Partial Differential Equations Representing Natural Phenomena". The program will run from July to August, 2028 (tentative).
This thematic program will follow the 3rd OIST-Oxford-SLMath Summer School which is scheduled to be held from June 26 - July 7, 2028 at the Okinawa Institute of Science and Technology (OIST). Information on upcoming and past summer schools of this series can be found here: https://www.oist.jp/research/research-units/apde/summer-schools .
Title: Singularities and Partial Differential Equations Representing Natural Phenomena
Theme of the Program: Comprehending a full characterization of singularities representing natural phenomena expressed by Partial Differential Equations (PDEs) is a major open problem in Mathematics and Modern Science. This thematic program will foster concentrated scientific activities in the following current research areas in Analysis & PDE:
- Potential Theory of Second-Order Elliptic and Parabolic PDEs
- Nonlinear Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
- Nonlinear Schrödinger Equations
- Nonlinear PDE Systems in Fluid Mechanics
The four areas of research outlined above have on their own an extremely well-established research history, as well as ambitious forward-looking plans. At the same time, however, important underlying common themes are recently emerging with an unusual recurrence. In this program, the organizers plan to enhance these common themes, facilitate a more uniform mathematical language, and ultimately initiate collaborations that otherwise would not have started. This research program will generate significant interdisciplinary activities with other fields of mathematics and other sciences and engineering such as probability theory and stochastic processes, multiscale numerical analysis, fluid mechanics and biomedical engineering.
Program Coordinators
Ugur G. Abdulla (OIST)
Gui-Qiang G. Chen (OxPDE, University of Oxford)
Suncica Canic (University of California, Berkeley)
Donatella Danielli (Arizona State University)
Zoran Grujic (University of Alabama at Birmingham)
Gigliola Staffilani (Massachusetts Institute of Technology)
Tentative Schedule
Week 1-3: Introductory talks, setting stage for the thematic program, continuation of the vision outlined in the previous SLMath workshop through discussion groups and individual seminar talks
Week 4: Workshop, demonstrating new/updated perspective potentially connecting approaches of the four main sub-fields, laying forward a new vision
Week 5-8: Moving forward with new vision through work in discussion groups, individual seminar talks